5 problems

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Kowalski–Zywina conjecture on the Chebotarev invariant
Kowalski–Zywina conjecture. For every finite group $G$ ,
Conjecturesolvedchebotarev-invariant finite-groups invariable-generationarXiv posted 2 days ago
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The Boston–Shalev conjecture on the Chebotarev invariant
Boston–Shalev conjecture. There is an absolute constant such that
Conjecturesolvedchebotarev-invariant finite-groups invariable-generationarXiv posted 2 days ago
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Guralnick–Shareshian–Woodroofe's prime-power and prime order generation question for alternating groups
Guralnick–Shareshian–Woodroofe's question. Is $A_n$ invariably generated by an element of order $p^a$ together with an element of order $r$ ?
Problemopenalternating-groups finite-groups invariable-generationarXiv posted 2 days ago
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Dixon's conjecture on invariable generation of transitive subgroups
Let $S_n$ be the symmetric group on $n$ points. Choose independent uniformly random permutations from $S_n$ , and let the average number required to invariably generate a transitive…
Conjectureopeninvariable-generation permutation-groups random-groupsarXiv posted 2 days ago
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Invariable generation conjecture for finite classical groups
Invariable generation conjecture. There exists a positive constant $k>0$ such that
Conjectureopenclassical-groups finite-groups invariable-generationarXiv posted 2 days ago

Kowalski–Zywina conjecture on the Chebotarev invariant